A force F applied to an object of mass m1 produces an acceleration of 3.10 m/s2.?

Question

A force F applied to an object of mass m1 produces an acceleration of 3.10 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.20 m/s2. If m1 and m2 are combined, what is their acceleration under the action of the force F.

Answer 1

First, define the force equations governing the 2 masses separately.

F = m_1*(3.1) ------------ (1)
F = m_2*(1.2) -------------(2)

Now you want to find the acceleration when the same force is acted on a mass that is the sum of the original two. Thus,

F = (m_1+m_2)*a --------------> solving for 'a'

Use (1) and (2) to substitue for m_1 and m_2

F = ([F/3.1]+[F/1.2])*a ---------> now solver for 'a'

a = F/([F/3.1]+[F/1.2]) = 1/[(1/3.1) + (1/1.2)]

Simplifying, you get 1/[(3.1+1.2)/(3.1*1.2)] = [(3.1*1.2)/(3.1+1.2)]

thus, a = 0.87 m/s^2

Hope this helps

Answer 2

F1=F2 (newton's regulation=> F=ma A. F=m1a1 (by way of fact the rigidity is comparable) F=m2a2 F= 3.50 m/s2* m1 F=2m/s2 * m2 isolate this to m1= ? isolate this equation to m2=? F/3.50 m/s2=m1 F/2m/s2 = m2 to discover the ration of m1/m2 divide the 1st equation by using the 2d m1/m2= (F/3.50)/ (F/2) = (F/3.50) * (2/F) now crosse multiply and cancel out the F and your left with: = 2/3.5 =that's the respond for A B. you in looking m1 and m2 when you consider that F is comparable m1a1=m2a2 3.5m1=2m2 if isolate this to m2=> m2=(3.5/2)m1=a million.75m1 so which you will discover m1 use the ratio from A m1/m2=(2/3.5) now replace m2 as a million.75m1 into this equation m1/ (a million.75m1)=(2/3.5) and if u remedy it for m1 you will finally end up with m1=1kg replace that throughout to m2=a million.75m1 and you will finally end up with m2=a million.75kg now m1+m2= a million.75kg+1kg=2.75kg for brand spanking new acceleration F=(m1+m2)*a and from the question u can positioned the two m1a1=F or m2a2=F so m1a1= (m1+m2)*a a million* 3.5= 2.seventy 5 * a (3.5/2.seventy 5)m/s^2= a (there could be an effortless way, so in basic terms double examine if that's stable)

Answer 3

1. You forgot a question mark at the end!!

2. Work it out yourself !!

Answer 4

m1 = F/3.1, m2 = F/1.2
(m1 + m2)a = F(1/3.1 + 1/1.2)a = F
a = 1/(1/3.1+1/1.2)
a = 1.2*3.1/(1.2+3.1)